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Quantum Lernmatrix.

Andreas Wichert1

  • 1Department of Computer Science and Engineering, INESC-ID & Instituto Superior Técnico, University of Lisbon, 2740-122 Porto Salvo, Portugal.

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This study introduces a quantum Lernmatrix for efficient pattern storage and retrieval. A novel tree-like structure improves accuracy and reduces computational costs compared to conventional methods.

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Area of Science:

  • Quantum computing
  • Information theory
  • Machine learning

Background:

  • The Monte Carlo Lernmatrix stores binary sparse coded patterns.
  • Quantum superposition offers potential for efficient data representation.

Purpose of the Study:

  • To develop and demonstrate a quantum Lernmatrix.
  • To improve pattern recovery accuracy and efficiency.
  • To analyze the cost-effectiveness of quantum pattern storage.

Main Methods:

  • Implementation of a quantum Lernmatrix using qiskit.
  • Application of quantum counting of ones for pattern recovery.
  • Introduction of a tree-like structure to enhance accuracy.
  • Analysis of loading costs for sparse patterns into quantum states.

Main Results:

  • Demonstration of the quantum Lernmatrix using qiskit experiments.
  • Identification of inaccuracies in Trugenberger's temperature parameter assumption.
  • Validation of the tree-like structure for improved correct answer identification.
  • Significant reduction in loading costs for sparse patterns compared to individual storage.

Conclusions:

  • The quantum Lernmatrix offers a more efficient approach to pattern storage and retrieval.
  • The proposed tree-like structure enhances the performance of quantum Lernmatrices.
  • Quantum Lernmatrices provide a computationally advantageous alternative to conventional methods and Grover's algorithm for specific tasks.